Diagrammar and metamorphosis of coset symmetries in dimensionally reduced type IIB supergravity

Studying the reduction of type IIB supergravity from ten to three spacetime dimensions, we describe the metamorphosis of the Dynkin diagram for gravity line “caterpillar” into a type IIB supergravity “ dragonfly” that is triggered by the inclusion of scalars and antisymmetric tensor fields. The final diagram corresponds to type IIB string theory E₈ global symmetry group, which is the subgroup of the conjectured E₁₁ hidden symmetry group. Application of the results for getting the type IIA/IIB T-duality rules and for searching for type IIB vacua solutions is considered.